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Peter Gao

Publications and source records attributed to Peter Gao.

At least 73 records · Page 4Linked to original sources

The Hazy and Metal-Rich Atmosphere of GJ 1214 b Constrained by Near and Mid-Infrared Transmission Spectroscopy

The near-infrared transmission spectrum of the warm sub-Neptune exoplanet GJ 1214 b has been observed to be flat and featureless, implying a high metallicity atmosphere with abundant aerosols. Recent JWST MIRI LRS observations of a phase curve of GJ 1214 b showed that its transmission spectrum is flat out into the mid-infrared. In this paper, we use the combined near- and mid-infrared transmission spectrum of GJ 1214 b to constrain its atmospheric composition and aerosol properties. We generate a grid of photochemical haze models using an aerosol microphysics code for a number of background atmospheres spanning metallicities from 100 to 1000 $\times$ solar, as well as a steam atmosphere scenario. The flatness of the combined data set largely rules out atmospheric metallicities $\leq$300 $\times$ solar due to their large corresponding molecular feature amplitudes, preferring values $\geq$1000 $\times$ solar and column haze production rates $\geq$10$^{-10}$ g cm$^{-2}$ s$^{-1}$. The steam atmosphere scenario with similarly high haze production rates also exhibit sufficiently small molecular features to be consistent with the transmission spectrum. These compositions imply that atmospheric mean molecular weights $\geq$15 g mol$^{-1}$ are needed to fit the data. Our results suggest that haze production is highly efficient on GJ 1214 b and could involve non-hydrocarbon, non-nitrogen haze precursors. Further characterization of GJ 1214 b's atmosphere would likely require multiple transits and eclipses using JWST across the near and mid-infrared, potentially complemented by groundbased high resolution transmission spectroscopy.

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Photochemically-produced SO$_2$ in the atmosphere of WASP-39b

Photochemistry is a fundamental process of planetary atmospheres that regulates the atmospheric composition and stability. However, no unambiguous photochemical products have been detected in exoplanet atmospheres to date. Recent observations from the JWST Transiting Exoplanet Early Release Science Program found a spectral absorption feature at 4.05 $μ$m arising from SO$_2$ in the atmosphere of WASP-39b. WASP-39b is a 1.27-Jupiter-radii, Saturn-mass (0.28 M$_J$) gas giant exoplanet orbiting a Sun-like star with an equilibrium temperature of $\sim$1100 K. The most plausible way of generating SO$_2$ in such an atmosphere is through photochemical processes. Here we show that the SO$_2$ distribution computed by a suite of photochemical models robustly explains the 4.05 $μ$m spectral feature identified by JWST transmission observations with NIRSpec PRISM (2.7$σ$) and G395H (4.5$σ$). SO$_2$ is produced by successive oxidation of sulphur radicals freed when hydrogen sulphide (H$_2$S) is destroyed. The sensitivity of the SO$_2$ feature to the enrichment of the atmosphere by heavy elements (metallicity) suggests that it can be used as a tracer of atmospheric properties, with WASP-39b exhibiting an inferred metallicity of $\sim$10$\times$ solar. We further point out that SO$_2$ also shows observable features at ultraviolet and thermal infrared wavelengths not available from the existing observations.

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A First Look at the JWST MIRI/LRS Phase Curve of WASP-43b

We observed a full-orbit phase curve of the hot Jupiter WASP-43b with MIRI/LRS as part of the Transiting Exoplanet Community Early Release Science Program. Here we report preliminary findings for the instrument performance from the team's MIRI Working Group. Overall we find that MIRI's performance for phase curve observations is excellent, with a few minor caveats. The key takeaways for Cycle 2 planning with MIRI/LRS are: (1) long-duration observations (> 24 hours) have now been successfully executed; (2) for phase curves, we recommend including a one-hour burn-in period prior to taking science data to mitigate the effects of the ramp systematic; and (3) we do not yet recommend partial phase curve observations. In addition, we also find that: the position of the spectrum on the detector is stable to within 0.03 pixels over the full 26.5-hour observation; the light curves typically show a systematic downward ramp that is strongest for the first 30 minutes, but continues to decay for hours; from 10.6-11.8 microns, the ramp effect has remarkably different behavior, possibly due to a different illumination history for the affected region of the detector; after trimming the integrations most affected by the initial ramps and correcting the remaining systematics with analytic models, we obtain residuals to the light-curve fits that are typically within 25% of the photon noise limit for 0.5-micron spectroscopic bins; non-linearity correction is not a significant source of additional noise for WASP-43, though it may be an issue for brighter targets; the gain value of 5.5 electrons/DN currently on CRDS and JDox is known to be incorrect, and the current best estimate for the gain is approximately 3.1 electrons/DN; new reference files for the JWST calibration pipeline reflecting these findings are under development at STScI.

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The effect of interior heat flux on the atmospheric circulation of hot and ultra-hot Jupiters

Many hot and ultra-hot Jupiters have inflated radii, implying that their interiors retain significant entropy from formation. These hot interiors lead to an enhanced internal heat flux that impinges upon the atmosphere from below. In this work, we study the effect of this hot interior on the atmospheric circulation and thermal structure of hot and ultra-hot Jupiters. To do so, we incorporate the population-level predictions from evolutionary models of hot and ultra-hot Jupiters as input for a suite of General Circulation Models (GCMs) of their atmospheric circulation with varying semi-major axis and surface gravity. We conduct simulations with and without a hot interior, and find that there are significant local differences in temperature of up to hundreds of Kelvin and in wind speeds of hundreds of m s$^{-1}$ or more across the observable atmosphere. These differences persist throughout the parameter regime studied, and are dependent on surface gravity through the impact on photosphere pressure. These results imply that the internal evolution and atmospheric thermal structure and dynamics of hot and ultra-hot Jupiters are coupled. As a result, a joint approach including both evolutionary models and GCMs may be required to make robust predictions for the atmospheric circulation of hot and ultra-hot Jupiters.

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Early Release Science of the exoplanet WASP-39b with JWST NIRCam

Measuring the metallicity and carbon-to-oxygen (C/O) ratio in exoplanet atmospheres is a fundamental step towards constraining the dominant chemical processes at work and, if in equilibrium, revealing planet formation histories. Transmission spectroscopy provides the necessary means by constraining the abundances of oxygen- and carbon-bearing species; however, this requires broad wavelength coverage, moderate spectral resolution, and high precision that, together, are not achievable with previous observatories. Now that JWST has commenced science operations, we are able to observe exoplanets at previously uncharted wavelengths and spectral resolutions. Here we report time-series observations of the transiting exoplanet WASP-39b using JWST's Near InfraRed Camera (NIRCam). The long-wavelength spectroscopic and short-wavelength photometric light curves span 2.0 - 4.0 $μ$m, exhibit minimal systematics, and reveal well-defined molecular absorption features in the planet's spectrum. Specifically, we detect gaseous H$_2$O in the atmosphere and place an upper limit on the abundance of CH$_4$. The otherwise prominent CO$_2$ feature at 2.8 $μ$m is largely masked by H$_2$O. The best-fit chemical equilibrium models favour an atmospheric metallicity of 1-100$\times$ solar (i.e., an enrichment of elements heavier than helium relative to the Sun) and a sub-stellar carbon-to-oxygen (C/O) ratio. The inferred high metallicity and low C/O ratio may indicate significant accretion of solid materials during planet formation or disequilibrium processes in the upper atmosphere.

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Early Release Science of the exoplanet WASP-39b with JWST NIRISS

Transmission spectroscopy provides insight into the atmospheric properties and consequently the formation history, physics, and chemistry of transiting exoplanets. However, obtaining precise inferences of atmospheric properties from transmission spectra requires simultaneously measuring the strength and shape of multiple spectral absorption features from a wide range of chemical species. This has been challenging given the precision and wavelength coverage of previous observatories. Here, we present the transmission spectrum of the Saturn-mass exoplanet WASP-39b obtained using the SOSS mode of the NIRISS instrument on the JWST. This spectrum spans $0.6 - 2.8 μ$m in wavelength and reveals multiple water absorption bands, the potassium resonance doublet, as well as signatures of clouds. The precision and broad wavelength coverage of NIRISS-SOSS allows us to break model degeneracies between cloud properties and the atmospheric composition of WASP-39b, favoring a heavy element enhancement ("metallicity") of $\sim 10 - 30 \times$ the solar value, a sub-solar carbon-to-oxygen (C/O) ratio, and a solar-to-super-solar potassium-to-oxygen (K/O) ratio. The observations are best explained by wavelength-dependent, non-gray clouds with inhomogeneous coverage of the planet's terminator.

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Hazy with a chance of star spots: constraining the atmosphere of the young planet, K2-33b

Although all-sky surveys have led to the discovery of dozens of young planets, little is known about their atmospheres. Here, we present multi-wavelength transit data for the super Neptune-sized exoplanet, K2-33b -- the youngest (~10 Myr) transiting exoplanet to-date. We combined photometric observations of K2-33 covering a total of 33 transits spanning >2 years, taken from K2, MEarth, Hubble, and Spitzer. The transit photometry spanned from the optical to the near-infrared (0.6-4.5$μ$m), enabling us to construct a transmission spectrum of the planet. We find that the optical transit depths are nearly a factor of two deeper than those from the near-infrared. This difference holds across multiple datasets taken over years, ruling out issues of data analysis and unconstrained systematics. Surface inhomogeneities on the young star can reproduce some of the difference, but required spot coverage fractions (>60%) are ruled out by the observed stellar spectrum(<20%). We find a better fit to the transmission spectrum using photochemical hazes, which were predicted to be strong in young, moderate-temperature, and large-radius planets like K2-33b. A tholin haze with CO as the dominant gaseous carbon carrier in the atmosphere can reasonably reproduce the data with small or no stellar surface inhomogeneities, consistent with the stellar spectrum. The HST data quality is insufficient for the detection of any molecular features. More observations would be required to fully characterize the hazes and spot properties and confirm the presence of CO suggested by current data.

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Depletion of gaseous CO in protoplanetary disks by surface-energy-regulated ice formation

Empirical constraints of fundamental properties of protoplanetary disks are essential for understanding planet formation and planetary properties (1,2). Carbon monoxide (CO) gas is often used to constrain disk properties (3). However, estimates show that the CO gas abundance in disks is depleted relative to expected values (4,5,6,7), and models of various disk processes impacting the CO abundance could not explain this depletion on observed 1Myr timescales (8,9,10,11,12,13,14). Here we demonstrate that surface energy effects on particles in disks, such as the Kelvin effect, that arise when ice heterogeneously nucleates onto an existing particle can efficiently trap CO in its ice phase. In previous ice formation models, CO gas was released when small ice-coated particles were lofted to warmed disk layers. Our model can reproduce the observed abundance, distribution and time evolution of gaseous CO in the four most studied protoplanetary disks (7). We constrain the solid and gaseous CO inventory at the midplane and disk diffusivities and resolve inconsistencies in estimates of the disk mass -- three crucial parameters that control planetary formation.

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Identification of carbon dioxide in an exoplanet atmosphere

Carbon dioxide (CO2) is a key chemical species that is found in a wide range of planetary atmospheres. In the context of exoplanets, CO2 is an indicator of the metal enrichment (i.e., elements heavier than helium, also called "metallicity"), and thus formation processes of the primary atmospheres of hot gas giants. It is also one of the most promising species to detect in the secondary atmospheres of terrestrial exoplanets. Previous photometric measurements of transiting planets with the Spitzer Space Telescope have given hints of the presence of CO2 but have not yielded definitive detections due to the lack of unambiguous spectroscopic identification. Here we present the detection of CO2 in the atmosphere of the gas giant exoplanet WASP-39b from transmission spectroscopy observations obtained with JWST as part of the Early Release Science Program (ERS). The data used in this study span 3.0 to 5.5 μm in wavelength and show a prominent CO2 absorption feature at 4.3 μm (26σ significance). The overall spectrum is well matched by one-dimensional, 10x solar metallicity models that assume radiative-convective-thermochemical equilibrium and have moderate cloud opacity. These models predict that the atmosphere should have water, carbon monoxide, and hydrogen sulfide in addition to CO2, but little methane. Furthermore, we also tentatively detect a small absorption feature near 4.0 μm that is not reproduced by these models.

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AU Microscopii in the FUV: Observations in Quiescence, During Flares, and Implications for AU Mic b and c

High energy X-ray and ultraviolet (UV) radiation from young stars impacts planetary atmospheric chemistry and mass loss. The active $\sim 22$ Myr M dwarf AU Mic hosts two exoplanets orbiting interior to its debris disk. Therefore, this system provides a unique opportunity to quantify the effects of stellar XUV irradiation on planetary atmospheres as a function of both age and orbital separation. In this paper we present over 5 hours of Far-UV (FUV) observations of AU Mic taken with the Cosmic Origins Spectrograph (COS; 1070-1360 Angstrom) on the Hubble Space Telescope (HST). We provide an itemization of $120$ emission features in the HST/COS FUV spectrum and quantify the flux contributions from formation temperatures ranging from $10^4-10^7$ K. We detect 13flares in the FUV white-light curve with energies ranging from $10^{29} - 10^{31}$ ergs. The majority of the energy in each of these flares is released from the transition region between the chromosphere and the corona. There is a 100$\times$ increase in flux at continuum wavelengths $λ< 1100$ Angstrom in each flare which may be caused by thermal Bremsstrahlung emission. We calculate that the baseline atmospheric mass-loss rate for AU Mic b is $\sim 10^8$ g s$^{-1}$, although this rate can be as high as $\sim 10^{14}$ g s$^{-1}$ during flares with $L_\textrm{flare} \simeq 10^{33}$ erg s$^{-1}$. Finally, we model the transmission spectra for AU Mic b and c with a new panchromatic spectrum of AU Mic c and motivate future JWST observations of these planets.

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Atmospheric Monitoring and Precise Spectroscopy of the HR 8799 Planets with SCExAO/CHARIS

The atmospheres of gas giant planets are thought to be inhomogeneous due to weather and patchy clouds. We present two full nights of coronagraphic observations of the HR 8799 planets using the CHARIS integral field spectrograph behind the SCExAO adaptive optics system on the Subaru Telescope to search for spectrophomometric variability. We did not detect significant variability signals, but placed the lowest variability upper limits for HR 8799 c and d. Based on injection-recovery tests, we expected to have a 50% chance to detect signals down to 10% H-band photometric variability for HR 8799 c and down to 30% H-band variability for HR 8799 d. We also investigated spectral variability and expected a 50% chance to recovery 20% variability in the H/K flux ratio for HR 8799 c. We combined all the data from the two nights to obtain some of the most precise spectra obtained for HR 8799 c, d, and e. Using a grid of cloudy radiative-convective-thermochemical equilibrium models, we found all three planets prefer supersolar metallicity with effective temperatures of ~1100 K. However, our high signal-to-noise spectra show that HR 8799 d has a distinct spectrum from HR 8799 c, possibly preferring more vertically extended and uniform clouds and indicating that the planets are not identical.

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The Hubble PanCET Program: A Featureless Transmission Spectrum for WASP-29b and Evidence of Enhanced Atmospheric Metallicity on WASP-80b

We present a uniform analysis of transit observations from the Hubble Space Telescope and Spitzer Space Telescope of two warm gas giants orbiting K-type stars - WASP-29b and WASP-80b. The transmission spectra, which span 0.4-5.0 $μ$m, are interpreted using a suite of chemical equilibrium PLATON atmospheric retrievals. Both planets show evidence of significant aerosol opacity along the day-night terminator. The spectrum of WASP-29b is flat throughout the visible and near-infrared, suggesting the presence of condensate clouds extending to low pressures. The lack of spectral features hinders our ability to constrain the atmospheric metallicity and C/O ratio. In contrast, WASP-80b shows a discernible, albeit muted H$_2$O absorption feature at 1.4 $μ$m, as well as a steep optical spectral slope that is caused by fine-particle aerosols and/or contamination from unocculted spots on the variable host star. WASP-80b joins the small number of gas-giant exoplanets that show evidence for enhanced atmospheric metallicity: the transmission spectrum is consistent with metallicities ranging from $\sim$30-100 times solar in the case of cloudy limbs to a few hundred times solar in the cloud-free scenario. In addition to the detection of water, we infer the presence of CO$_2$ in the atmosphere of WASP-80b based on the enhanced transit depth in the Spitzer 4.5 $μ$m bandpass. From a complementary analysis of Spitzer secondary eclipses, we find that the dayside emission from WASP-29b and WASP-80b is consistent with brightness temperatures of $937 \pm 48$ and $851 \pm 14$ K, respectively, indicating relatively weak day-night heat transport and low Bond albedo.

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Patchy nightside clouds on ultra-hot Jupiters: General Circulation Model simulations with radiatively active cloud tracers

The atmospheres of ultra-hot Jupiters have been characterized in detail through recent phase curve and low- and high-resolution emission and transmission spectroscopic observations. Previous numerical studies have analyzed the effect of the localized recombination of hydrogen on the atmospheric dynamics and heat transport of ultra-hot Jupiters, finding that hydrogen dissociation and recombination lead to a reduction in the day-to-night contrasts of ultra-hot Jupiters relative to previous expectations. In this work, we add to previous efforts by also considering the localized condensation of clouds in the atmospheres of ultra-hot Jupiters, their resulting transport by the atmospheric circulation, and the radiative feedback of clouds on the atmospheric dynamics. To do so, we include radiatively active cloud tracers into the existing MITgcm framework for simulating the atmospheric dynamics of ultra-hot Jupiters. We take cloud condensate properties appropriate for the high-temperature condensate corundum from CARMA cloud microphysics models. We conduct a suite of GCM simulations with varying cloud microphysical and radiative properties, and we find that partial cloud coverage is a ubiquitous outcome of our simulations. This patchy cloud distribution is inherently set by atmospheric dynamics in addition to equilibrium cloud condensation, and causes a cloud greenhouse effect that warms the atmosphere below the cloud deck. Nightside clouds are further sequestered at depth due to a dynamically induced high-altitude thermal inversion. We post-process our GCMs with the Monte Carlo radiative transfer code gCMCRT and find that the patchy clouds on ultra-hot Jupiters do not significantly impact transmission spectra but can affect their phase-dependent emission spectra.

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Transit Timing Variations for AU Microscopii b & c

We explore the transit timing variations (TTVs) of the young (22 Myr) nearby AU Mic planetary system. For AU Mic b, we introduce three Spitzer (4.5 $μ$m) transits, five TESS transits, 11 LCO transits, one PEST transit, one Brierfield transit, and two transit timing measurements from Rossiter-McLaughlin observations; for AU Mic c, we introduce three TESS transits. We present two independent TTV analyses. First, we use EXOFASTv2 to jointly model the Spitzer and ground-based transits and to obtain the midpoint transit times. We then construct an O--C diagram and model the TTVs with Exo-Striker. Second, we reproduce our results with an independent photodynamical analysis. We recover a TTV mass for AU Mic c of 10.8$^{+2.3}_{-2.2}$ M$_{E}$. We compare the TTV-derived constraints to a recent radial-velocity (RV) mass determination. We also observe excess TTVs that do not appear to be consistent with the dynamical interactions of b and c alone, and do not appear to be due to spots or flares. Thus, we present a hypothetical non-transiting "middle-d" candidate exoplanet that is consistent with the observed TTVs, the candidate RV signal, and would establish the AU Mic system as a compact resonant multi-planet chain in a 4:6:9 period commensurability. These results demonstrate that the AU Mic planetary system is dynamically interacting producing detectable TTVs, and the implied orbital dynamics may inform the formation mechanisms for this young system. We recommend future RV and TTV observations of AU Mic b and c to further constrain the masses and to confirm the existence of possible additional planet(s).

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A close-in puffy Neptune with hidden friends: The enigma of TOI 620

We present the validation of a transiting low-density exoplanet orbiting the M2.5 dwarf TOI 620 discovered by the NASA TESS mission. We utilize photometric data from both TESS and ground-based follow-up observations to validate the ephemerides of the 5.09-day transiting signal and vet false positive scenarios. High-contrast imaging data are used to resolve the stellar host and exclude stellar companions at separations $\gtrsim 0.2''$. We obtain follow-up spectroscopy and corresponding precise radial velocities (RVs) with multiple PRV spectrographs to confirm the planetary nature of the transiting exoplanet. We calculate a 5$σ$ upper limit of $M_P < 7.1$ M$_\oplus$ and $ρ_P < 0.74$ g cm$^{-3}$, and we identify a non-transiting 17.7-day candidate. We also find evidence for a substellar (1-20 M$_{\rm J}$) companion with a projected separation $\lesssim 20$ au from a combined analysis of Gaia, AO imaging, and RVs. With the discovery of this outer companion, we carry out a detailed exploration of the possibilities that TOI 620 b might instead be a circum-secondary planet or a pair of eclipsing binary stars orbiting the host in a hierarchical triple system. We find, under scrutiny, that we can exclude both of these scenarios from the multi-wavelength transit photometry, thus validating TOI 620 b as a low-density exoplanet transiting the central star in this system. The low density of TOI 620 b makes it one of the most amenable exoplanets for atmospheric characterization, such as with JWST and Ariel, validated or confirmed by the TESS mission to date.

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Microphysics of Water Clouds in the Atmospheres of Y Dwarfs and Temperate Giant Planets

Water clouds are expected to form on Y dwarfs and giant planets with equilibrium temperatures near or below that of Earth, drastically altering their atmospheric compositions and their albedos and thermal emission spectra. Here we use the 1D Community Aerosol and Radiation Model for Atmospheres (CARMA) to investigate the microphysics of water clouds on cool substellar worlds to constrain their typical particle sizes and vertical extent, taking into consideration nucleation and condensation, which have not been considered in detail for water clouds in H/He atmospheres. We compute a small grid of Y dwarf and temperate giant exoplanet atmosphere models with water clouds forming through homogeneous nucleation and heterogeneous nucleation on cloud condensation nuclei composed of meteoritic dust, organic photochemical hazes, and upwelled potassium chloride cloud particles. We present comparisons with the Ackerman & Marley parameterization of cloud physics to extract the optimal sedimentation efficiency parameter (f$_{sed}$) using Virga. We find that no Virga model replicates the CARMA water clouds exactly and that a transition in f$_{sed}$ occurs from the base of the cloud to the cloud top. Furthermore, we generate simulated thermal emission and geometric albedo spectra and find large, wavelength-dependent differences between the CARMA and Virga models, with different gas absorption bands reacting differently to the different cloud distributions and particularly large differences in the M band. Therefore, constraining the vertically-dependent properties of water clouds will be essential to estimating the gas abundances in these atmospheres.

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The First Near-Infrared Transmission Spectrum of HIP 41378 f, a Low-Mass Temperate Jovian World in a Multi-Planet System

We present a near-infrared transmission spectrum of the long period (P=542 days), temperate ($T_{eq}$=294 K) giant planet HIP 41378 f obtained with the Wide-Field Camera 3 (WFC3) instrument aboard the Hubble Space Telescope (HST). With a measured mass of 12 $\pm$ 3 $M_{\oplus}$ and a radius of 9.2 $\pm$ 0.1 $R_{\oplus}$, HIP 41378 f has an extremely low bulk density (0.09 $\pm$ 0.02 g/cm$^{3}$). We measure the transit depth with a median precision of 84 ppm in 30 spectrophotometric channels with uniformly-sized widths of 0.018 microns. Within this level of precision, the spectrum shows no evidence of absorption from gaseous molecular features between 1.1-1.7 microns. Comparing the observed transmission spectrum to a suite of 1D radiative-convective-thermochemical-equilibrium forward models, we rule out clear, low-metallicity atmospheres and find that the data prefer high-metallicity atmospheres or models with an additional opacity source such as high-altitude hazes and/or circumplanetary rings. We explore the ringed scenario for this planet further by jointly fitting the K2 and HST light curves to constrain the properties of putative rings. We also assess the possibility of distinguishing between hazy, ringed, and high-metallicity scenarios at longer wavelengths with JWST. HIP 41378 f provides a rare opportunity to probe the atmospheric composition of a cool giant planet spanning the gap between the Solar System giants, directly imaged planets, and the highly-irradiated hot Jupiters traditionally studied via transit spectroscopy.

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A bimodal distribution of haze in Pluto's atmosphere

Pluto, Titan, and Triton make up a unique class of solar system bodies, with icy surfaces and chemically reducing atmospheres rich in organic photochemistry and haze formation. Hazes play important roles in these atmospheres, with physical and chemical processes highly dependent on particle sizes, but the haze size distribution in reducing atmospheres is currently poorly understood. Here we report observational evidence that Pluto's haze particles are bimodally distributed, which successfully reproduces the full phase scattering observations from New Horizons. Combined with previous simulations of Titan's haze, this result suggests that haze particles in reducing atmospheres undergo rapid shape change near pressure levels ~0.5Pa and favors a photochemical rather than a dynamical origin for the formation of Titan's detached haze. It also demonstrates that both oxidizing and reducing atmospheres can produce multi-modal hazes, and encourages reanalysis of observations of hazes on Titan and Triton.

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